library(tigris)
To enable 
caching of data, set `options(tigris_use_cache = TRUE)` in your R script or .Rprofile.
library(data.table)
Registered S3 method overwritten by 'data.table':
  method           from
  print.data.table     
data.table 1.14.2 using 3 threads (see ?getDTthreads).  Latest news: r-datatable.com

Census 2010-2021 Counties VA, DC, MD

for (i in 10:21) {
  yr <- as.integer(paste0(20, i))
  counties <- counties(state = c("51", "11", "24"), cb = FALSE, year = yr)
  counties$geometry <- NULL
  assign(paste0("dc.counties.", yr), setDT(counties))
}

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if(exists("dt_out")) rm(dt_out)
for (i in 10:21) {
  yr <- as.integer(paste0(20, i))
  cols <- colnames(get(paste0("dc.counties.", yr)))
  cols <- cols[cols %like% "GEOID" | cols %like% "NAMELSAD"]
  dt <- get(paste0("dc.counties.", yr))
  select_cols <- dt[ , cols, with=FALSE]
  colnames(select_cols) <- c("geoid", "region_name")
  select_cols$year <- yr
  
  if(exists("dt_out")) dt_out <- rbindlist(list(dt_out, select_cols))
  else dt_out <- select_cols
}
dc_county_names <- dt_out

dc_county_names[geoid %like% "^51", region_name := paste0(region_name, ", Virginia")]
dc_county_names[geoid %like% "^24", region_name := paste0(region_name, ", Maryland")]

Census 2010-2021 Census Tracts VA, DC, MD

for (i in 10:21) {
  yr <- as.integer(paste0(20, i))
  state_fips <- c("51", "11", "24")
  if(exists("dt_out")) rm(dt_out)
  for (s in state_fips) {
    state_tracts <- tracts(state = s, year = yr)
    state_tracts$geometry <- NULL
    setDT(state_tracts)
    if(exists("dt_out")) dt_out <- rbindlist(list(dt_out, state_tracts))
    else dt_out <- state_tracts
  }
  assign(paste0("dc.tracts.", yr), dt_out)
}
if(exists("dt_out")) rm(dt_out)
for (i in 10:21) {
  yr <- as.integer(paste0(20, i))
  cols <- colnames(get(paste0("dc.tracts.", yr)))
  cols <- cols[cols %like% "GEOID" | cols %like% "NAMELSAD"]
  dt <- get(paste0("dc.tracts.", yr))
  select_cols <- dt[ , cols, with=FALSE]
  colnames(select_cols) <- c("geoid", "region_name")
  select_cols$year <- yr
  
  if(exists("dt_out")) dt_out <- rbindlist(list(dt_out, select_cols))
  else dt_out <- select_cols
}
dc_tract_names <- dt_out

Census 2010-2021 Census Block Groups VA, DC, MD

state_county_fips <- data.table(geoid_st = substr(dc_counties_unq$geoid, 1, 2),
                                geoid_ct = substr(dc_counties_unq$geoid, 3, 5))

if(exists("dt_out")) rm(dt_out)
for (i in 10:21) {
  yr <- as.integer(paste0(20, i))
  for (i in 1:nrow(state_county_fips)) {
    bgs <- block_groups(state = state_county_fips[i, geoid_st],
                        county = state_county_fips[i, geoid_ct],
                        year = yr)
    bgs$geometry <- NULL
    setDT(bgs)
    cols <- colnames(bgs)
    cols <- cols[cols %like% "GEOID" | cols %like% "NAMELSAD"]
    select_cols <- bgs[ , cols, with=FALSE]
    colnames(select_cols) <- c("geoid", "region_name")
    select_cols$year <- yr
    
    if (exists("dt_out")) dt_out <- rbindlist(list(dt_out, select_cols))
    else dt_out <- select_cols
  }
}

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dc_block_groups <- dt_out

Combine

Write to DB

con <- get_db_conn()
dc_dbWriteTable(con, "dc_geographies", "ncr_cttrbg_tiger_2010_2020_geo_names", census_geo_names)
[1] TRUE
<PostgreSQLResult>
DBI::dbDisconnect(con)
[1] TRUE
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